Typically abcesses do happen in the hoof to horses, but an abcess can happen anywhere. Any kind of injury where the skin is broken has to potential to abcess, and an abcess can be life threatening. Doesn't exactly sound like that type of an abcess though. If they are just spontaneously popping up and growing it sounds like there is an underlying factor. I don't know if you have pigeon fever in your area but maybe you should check this link out.
PIGEON FEVER in Horses
Kinda sounds like it, but you would be a better judge of the symptoms. In any case, call the vet. There is infection coming from somewhere and it could get serious quickly. Keep us updated!